The twin-engine turboprop was flying from Cascavel in the southern state of Paraná to Guarulhos airport in São Paulo city when it came down in the town of Vinhedo, Voepass airline says.
Footage circulating on social media shows a plane descending vertically, spiralling as it falls.
The ATR 72-500 was carrying 57 passengers and four crew. Local authorities say there were no survivors.
Brazil’s President, Luiz Inácio Lula da Silva, expressed solidarity with the families and friends of the victims.
São Paulo’s state Governor, Tarcísio Gomes de Freitas, declared three days of mourning.
The authorities said the flight recorders had been retrieved. ATR, the French-Italian plane maker, said it would co-operate with the investigation.
The plane landed in a residential area but no-one on the ground was injured.
Officials say only one home in a local condominium complex was damaged.
Video showed a large area on fire and smoking wreckage in an area full of houses.
Police and fire services are at the scene.
According to tracking website Flightradar24, the plane left Cascavel at 11:56 local time (14:56 GMT). The last signal received from the aircraft was about an hour and a half later.
Brazil’s civil aviation agency said the plane, which was built in 2010, had been “in good operating condition, with valid registration and airworthiness certificates”.
The four crew members on board at the time of the accident were all duly licensed and had valid qualifications, it added.
The Uopeccan Cancer Hospital in Cascavel told BBC Brasil that two of its trainee doctors were among the passengers who died.
The moment the passenger plane crashed was witnessed by local residents.
“When I heard the sound of the plane falling, I looked out my window at home and saw the moment it crashed,” Felipe Magalhaes told Reuters news agency, adding that the sight had left him “terrified”.
Another resident, Nathalie Cicari, told CNN Brasil she had been having lunch when she heard a “very loud noise very close by”, describing it like the sound of a drone but “much louder”.
“I went out on the balcony and saw the plane spinning. Within seconds, I realised that it was not a normal movement for a plane.”
It is Brazil’s worst plane crash since 2007, when a TAM Express plane crashed and burst into flames at São Paulo’s Congonhas airport, killing 199 people.
President Lula paid tribute to the victims at an event where he was speaking.
“I have to be the bearer of very bad news and I would like everyone to stand up so that we can have a minute of silence,” he told his audience.
He posted on social media that news of the crash was “very sad”. “All my solidarity to the families and friends of the victims,” he said.
The nearby town of Valinhos sent 20 emergency personnel to the crash site as part of a joint operation, local authorities said.
“Twenty men were mobilised, including three vehicles from the Valinhos Municipal Civil Guard and one vehicle from the Civil Defense,” Valinhos City Hall said in a statement.
ATR said in a statement that it had been informed of an accident involving an ATR 72-500.
“Our first thoughts are with all the individuals affected by this event,” it said.
“The ATR specialists are fully engaged to support both the investigation and the customer.”
(BBC)
